Archive for May, 2016

My activities as an engineering expert often involve creative problem solving of the sort we did in last week’s blog when we explored the interplay between work and kinetic energy. We used the Work-Energy Theorem to mathematically relate the kinetic energy in a piece of ceramic to the work performed by the friction that’s produced when it skids across a concrete floor. A new formula was derived which enables us to calculate the kinetic energy contained within the piece at the start of its slide by means of the work of friction. We’ll crunch numbers today to determine that quantity.

The formula we derived last time and that we’ll be working with today is,

Calculating Kinetic Energy By Means of the Work of Friction

where, KE is the ceramic piece’s kinetic energy,FF is the frictional force opposing its movement across the floor, and d is the distance it travels before friction between it and the less than glass-smooth floor brings it to a stop.

The numbers we’ll need to work the equation have been derived in previous blogs. We calculated the frictional force, FF, acting against a ceramic piece weighing 0.09 kilograms to be 0.35 kilogram-meters/second2 and the measured distance, d, it travels across the floor to be equal to 2 meters. Plugging in these values, we derive the following working equation,

KE = 0.35 kilogram-meters/second2 ×2 meters

KE = 0.70 kilogram-meters2/second2

The kinetic energy contained within that broken bit of ceramic is just about what it takes to light a 1 watt flashlight bulb for almost one second!

Now that we’ve determined this quantity, other energy quantities can also be calculated, like the velocity of the ceramic piece when it began its slide. We’ll do that next time.

We’ve been discussing the different forms energy takes, delving deeply into de Coriolis’ claim that energy doesn’t ever die or disappear, it simply changes forms depending on the tasks it’s performing. Today we’ll combine mathematical formulas to derive an equation specific to our needs, an activity my work as an engineering expert frequently requires of me. Our task today is to find a means to calculate the amount of kinetic energy contained within a piece of ceramic skidding across a concrete floor. To do so we’ll combine the frictional force and Work-Energy Theorem formulas to observe the interplay between work and kinetic energy.

As we learned studying the math behind the Work-Energy Theorem, it takes work to slow a moving object. Work is present in our example due to the friction that’s created when the broken piece moves across the floor. The formula to calculate the amount of work being performed in this situation is written as,

W = FF ×d (1)

where, d is the distance the piece travels before it stops, and FF is the frictional force that stops it.

We established last time that our ceramic piece has a mass of 0.09 kilograms and the friction created between it and the floor was calculated to be 0.35 kilogram-meters/second2. We’ll use this information to calculate the amount of kinetic energy it contains. Here again is the kinetic energy formula, as presented previously,

KE = ½ × m × v2 (2)

where m represents the broken piece’s mass and v its velocity when it first begins to move across the floor.

The Interplay of Work and Kinetic Energy

The Work-Energy Theorem states that the work,W, required to stop the piece’s travel is equal to its kinetic energy,KE, while in motion. This relationship is expressed as,

KE = W (3)

Substituting terms from equation (1) into equation (3), we derive a formula that allows us to calculate the kinetic energy of our broken piece if we know the frictional force, FF, acting upon it which causes it to stop within a distance, d,

KE = FF × d

Next time we’ll use this newly derived formula, and the value we found for FF in our previous article, to crunch numbers and calculate the exact amount of kinetic energy contained with our ceramic piece.